Kolloquium Mathematische Physik

Ever since the pioneering works of Wigner, Gaudin, Dyson, and Mehta, the correlations of eigenvalues of large random matrices on short scales have been a central topic in random matrix theory. On the microscopic spectral scale, comparable with the typical eigenvalue spacing, these correlations are now well understood for Wigner matrices thanks to the recent solution of the Wigner-Gaudin-Dyson-Mehta universality conjecture. In this talk I focus on eigenvalue density-density correlations between eigenvalues whose separation is much larger than the microscopic spectral scale; here the correlations are much weaker than on the microscopic scale. I discuss to what extent the Wigner-Gaudin-Dyson-Mehta universality remains valid on such larger scales, for Wigner matrices and random band matrices.

Seminar Hochenergiephysik

Several anomalies observed in neutrino oscillation experiments have
been interpreted as possible hints for the existence of eV-scale sterile
neutrinos. In this talk, we critically review these hints and present
results from comprehensive global fits. Our results reveal significant
tension in the global data set, which motivates us to discuss also
alternative explanations for the observed anomalies. In the final part
of the talk, we discuss cosmological constraints on light sterile
neutrinos and ways to avoid them.